After witnessing Manchester United succumb to a limp 2-0 defeat at his former club Everton, David Moyes' troubles show no sign of easing after it emerged that Danny Welbeck is considering his future at Old Trafford, with the England striker dismayed at his lack of opportunities to play as a striker and unsure of his relationship with the manager.

Welbeck came on as a second-half substitute at Goodison Park as United suffered their 11th Premier League defeat of the season. Arsenal and Tottenham Hotspur are interested in signing Welbeck in the close season. The player is aware of the clubs' interest and is weighing up his options as he is intent on ensuring his career does not stall .

Moyes refused to deny speculation that Welbeck is considering his options. Asked about the striker's intention to leave, the United manager said: "Danny Welbeck is really important to me and I really value him. There have been lots of stories. I can only tell you Danny Welbeck is really important to me and really important to Manchester United."

Welbeck will have two years left on his contract in the summer, the usual juncture when fresh terms would be offered. Yet the 23-year-old, who earns around £70,000 a-week, may decide against signing a new deal.

Earlier in the season Moyes claimed he had instructed Welbeck to stay behind for extra training, informing him to follow Wayne Rooney's example. He said: "I've got to say we had a word with him about a month ago and we said that he needs to be the last off the training field. Wayne's out there practising his finishing each day, whether it's taking free-kicks, shooting from tight angles or bending them in, whatever it may be Wayne's practising."

Yet Welbeck questioned Moyes' claim, saying: "I have been doing that ever since I have been at United. I have been injured this season so maybe the manager has not seen me on the training pitch as much."

Last week Moyes disciplined Welbeck, along with Tom Cleverley and Ashley Young, for a night out in Manchester following the Champions League exit to Bayern Munich. While United had no game for 10 days before Sunday's trip to Everton and the manager had given his squad three days off, the trio are thought to have contravened stipulations that they should not be out late within 48 hours of the tie.

If Welbeck was to leave it would be a significant blow. He is a lifelong United fan, who is from the city, and his unhappiness signals further disgruntlement within the squad. In January the Guardian reported that some senior players were uncertain of Moyes' credentials and with United in seventh and 10 points from a Champions League berth the questions remain.

Nemanja Vidic, the captain, has already announced he will depart in the summer and the futures of Rio Ferdinand and Patrice Evra are also in the balance. Javier Hernández, Shinji Kagawa, Darren Fletcher, Nani, Young, Cleverley, Alexander Büttner and Ryan Giggs are other members of Moyes's squad whose futures are likewise in doubt.